Stochastic partial differential equations for some measure-valued diffusions
We consider two classes of measure-valued diffusion processes, measure- valued branching diffusions and Fleming-Viot diffusion models. When the basic space is \(\mathbb R^ 1\), and the drift operator is a fractional Laplacian of order \(1<\alpha \leq 2\), we derive stochastic partial differential equations based on a space-time white noise for these two processes. The former is the expected one by Dawson, but the latter is a new type of stochastic partial differential equations.
scientific article; zbMATH DE number 4026474
scientific article